Most elegant, but rather inefficient:
([:q:^:_1 p:) a=: 1e7?.@#1e6
_
R.E. Boss
-----Oorspronkelijk bericht-----
Van: Programming <[email protected]> Namens
Schmidt-Gröttrup, Markus
Verzonden: dinsdag 30 oktober 2018 16:22
Aan: [email protected]
Onderwerp: Re: [Jprogramming] Intersection and Union of (multi)sets
Should be
IS=:+./&.([:q:^:_1 p:) NB. Intersection
UN=:*./&.([:q:^:_1 p:) NB. union
Markus S.-G.
-----Ursprüngliche Nachricht-----
Von: Programming <[email protected]> Im Auftrag von Don
Guinn
Gesendet: Dienstag, 30. Oktober 2018 15:46
An: Programming forum <[email protected]>
Betreff: Re: [Jprogramming] Intersection and Union of (multi)sets
Looks better.
UN=:+./&.([:q:^:_1 p:)
IS=:*./&.([:q:^:_1 p:)
1 2 3 3 3 UN 3 3 3 3 3 4 5 6
3 3 3
1 2 3 3 3 IS 3 3 3 3 3 4 5 6
1 2 3 3 3 3 3 4 5 6
On Tue, Oct 30, 2018 at 7:56 AM Don Guinn <[email protected]> wrote:
> You're right. The trick is to make them prime numbers. But it's not pretty.
>
> IS=:(_1 p:[:q:+.&([:*/[:p:]))/
>
> UN=:(_1 p:[:q:*.&([:*/[:p:]))/
>
> 1 2 3 3 3 UN 3 3 3 3 3 4 5 6
>
> 1 2 3 3 3 3 3 4 5 6
>
> 1 2 3 3 3 IS 3 3 3 3 3 4 5 6
> 3 3 3
>
> On Tue, Oct 30, 2018 at 4:58 AM 'Bo Jacoby' via Programming <
> [email protected]> wrote:
>
>>
>> IS=.+.&.(*/)
>>
>> UN=.*.&.(*/)
>>
>>
>> This still works for multisets of prime numbers.
>> Den tirsdag den 30. oktober 2018 11.55.04 CET skrev 'Bo Jacoby'
>> via Programming <[email protected]>:
>>
>>
>> IS=.[:q:+.&(*/)
>>
>> UN=.[:q:*.&(*/)
>> 2 3 3 5 IS 3 5 5 5
>> 3 5
>> 2 3 3 5 UN 3 5 5 5
>> 2 3 3 5 5 5
>> This works for multisets of PRIME numbers only.
>>
>>
>> Den tirsdag den 30. oktober 2018 10.46.17 CET skrev R.E. Boss <
>> [email protected]>:
>>
>> IMO we should interpret the intersection and the union of two
>> (multi)sets (sets X with X >:&# ~.X) in the same way as is done by
>> the GCD and the LCM of two numbers.
>> So for two numbers N and M with (multi)sets of primefactors A and B,
>> we should have (N +. M) = */(A IS B) and (N *. M) = */ (A UN B), with
>> IS=intersection and UN = union of the (multi)sets A and B.
>> Obviously we require (A IS B) =&(/:~) B IS A and also (A UN B)
>> =&(/:~) B UN A for all (multi)sets A and B.
>> E.g.
>> 1 2 3 3 3 IS 3 3 3 3 3 4 5 6
>> 3 3 3
>> 1 2 3 3 3 UN 3 3 3 3 3 4 5 6
>> 1 2 3 3 3 3 3 4 5 6
>>
>> What are elegant and efficient J-definitions for IS and UN?
>>
>>
>> I have constructed
>> UN_reb=: ([:(~.@{.#~ {. >.//.{:) |:@,&(({.,#)/.~)) and
>> IS_reb=: ([:(~.@{.#~ {. <.//.{:) ([|:@, ],~ 0,.~ -.~&:({."1),
>> -.&:({."1))&(({. , #)/.~))
>>
>> 1 2 3 3 3 UN_reb 3 3 3 3 3 4 5 6
>> 1 2 3 3 3 3 3 4 5 6
>> 1 2 3 3 3 IS_reb 3 3 3 3 3 4 5 6
>> 3 3 3
>> 1 2 3 3 3 UN_reb~ 3 3 3 3 3 4 5 6
>> 3 3 3 3 3 4 5 6 1 2
>> 1 2 3 3 3 IS_reb~ 3 3 3 3 3 4 5 6
>> 3 3 3
>>
>> a=: 1e7?.@#1e6
>> ts'a UN_reb a+499999'
>> 0.76631908 4.6996013e8
>> #a UN_reb a+49999
>> 12186812
>> ts'a IS_reb a+499999'
>> 0.76073743 3.3554592e8
>> #a IS_reb a+49999
>> 7813188
>>
>>
>> R.E. Boss
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>
>
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